Does the comp project use any synthetic logic ?
IMHO synlog is the basis of worldly intelligence.
.
Analytic logic can tell us nothing new, so cannot be a
basis alone for intelligence.

Machines have already both. As the classical definition of the knower
works for machine by incompleteness, making such a knower an
intuitionist thinker unable to have a name. Gödel's incompleteness
prevents all easy reductionist conception of machine.

The problem is that we define machines by their bodies, and bodies
don't think, only persons think. They are only locally incarnated
through bodies. This follows logically from the mechanist assumption.

Analytic statements are a special class of a priori statements. In
analytic statements, the predicate concept adds nothing to the
subject concept, e.g., “Bachelors are unmarried,” or “The red
house is red.”

Synthetic statements are a special class of a posteriori statements.
In synthetic statements, the predicate concept adds something to the
subject concept (the two concepts are synthesized), e.g., “The red
house is owned by a dentist.”

Hume’s Fork

According to Hume, legitimate reasoning has just two possible kinds
of subject matter:

1. Relations of Ideas (e.g., math, logic)
or
2. Matters of Fact (e.g., empirical matters).
Reasoning about relations of ideas is analytic and a priori.
Reasoning about matters of facts is synthetic and a posteriori.

For Hume, any legitimate statement is either analytic a priori or
synthetic a posteriori. According to Hume, analytic a priori
statements – the kind we use when we reason about relations of
ideas – tell us nothing about the world; they tell us only about
how we think and use language.

Thus, according to Hume, the only statements than can tell us
anything about the world are synthetic a posteriori. And according
to Hume, if a statement is synthetic a posteriori, it must be
grounded in impressions (sense data or passion). If no impressions
support a synthetic statement, the statement is bogus superstition,
and should be rejected.

In other words, Hume’s fork has two tines. Legitimate statements
are either

analytic a priori — like statements of math, which tell us nothing
about the external world; or

synthetic a posteriori — like statements about the world of the
senses, supportable by impressions (sense data or passions).

Thus, statements are either analytic a priori (in which case they
tell us nothing about the world), OR they are synthetic a posteriori
(in which case they must be supported by impressions). For Hume,
there are no other legitimate possibilities.

Hume’s fork means that statements about matters of fact always
require empirical support; we can never “just know” them. This is
why Hume criticizes the Ontological Argument, which attempts to
prove that the claim “God exists” is true a priori. For Hume, no
claim about existence can be a priori, since whether or not
something exists is a matter of fact, and thus must be known a
posteriori.

Hume’s Fork does not necessarily plunge us into skepticism about
morality, since for Hume, morality is a matter of the passions, and
passions are one of the sources of impressions. So to say “Stealing
is wrong” simply means “I feel stealing is wrong”; but what if
everybody feels the same way? Then morality is a set of objective
facts about human feeling based on common human nature. "

Roger Clough, rclo...@verizon.net
8/24/2012

Leibniz would say, "If there's no God, we'd have to invent him so
everything could function."

A quibble with the beginning of Richard's paper. On the first page
it says:

'It is beyond the scope of this paper and admittedly beyond my
understanding to delve into G鰀elian logic, which seems to be self-
referential proof by contradiction, except to mention that Penrose
in Shadows of the Mind(1994), as confirmed by David Chalmers(1995),
arrived at a seemingly valid 7 step proof that human 搑easoning
powers cannot be captured by any formal system�.'

"2.16 It is section 3.3 that carries the burden of this strand of
Penrose's argument, but unfortunately it seems to be one of the
least convincing sections in the book. By his assumption that the
relevant class of computational systems are all straightforward
axiom-and-rules system, Penrose is not taking AI seriously, and
certainly is not doing enough to establish his conclusion that
physics is uncomputable. I conclude that none of Penrose's argument
up to this point put a dent in the natural AI position: that our
reasoning powers may be captured by a sound formal system F, where
we cannot determine that F is sound."

Then when dealing with Penrose's "second argument", he says that
Penrose draws the wrong conclusions; where Penrose concludes that
our reasoning cannot be the product of any formal system, Chalmers
concludes that the actual issue is that we cannot be 100% sure our
reasoning is "sound" (which I understand to mean we can never be
100% sure that we have not made a false conclusion about whether all
the propositions we have proved true or false actually have that
truth-value in "true arithmetic"):

"3.12 We can see, then, that the assumption that we know we are
sound leads to a contradiction. One might try to pin the blame on
one of the other assumptions, but all these seem quite
straightforward. Indeed, these include the sort of implicit
assumptions that Penrose appeals to in his arguments all the time.
Indeed, one could make the case that all of premises (1)-(4) are
implicitly appealed to in Penrose's main argument. For the purposes
of the argument against Penrose, it does not really matter which we
blame for the contradiction, but I think it is fairly clear that it
is the assumption that the system knows that it is sound that causes
most of the damage. It is this assumption, then, that should be
withdrawn.

"3.13 Penrose has therefore pointed to a false culprit. When the
contradiction is reached, he pins the blame on the assumption that
our reasoning powers are captured by a formal system F. But the
argument above shows that this assumption is inessential in reaching
the contradiction: A similar contradiction, via a not dissimilar
sort of argument, can be reached even in the absence of that
assumption. It follows that the responsibility for the contradiction
lies elsewhere than in the assumption of computability. It is the
assumption about knowledge of soundness that should be withdrawn.

"3.14 Still, Penrose's argument has succeeded in clarifying some
issues. In a sense, it shows where the deepest flaw in G鰀elian
arguments lies. One might have thought that the deepest flaw lay in
the unjustified claim that one can see the soundness of certain
formal systems that underlie our own reasoning. But in fact, if the
above analysis is correct, the deepest flaw lies in the assumption
that we know that we are sound. All G鰀elian arguments appeal to
this premise somewhere, but in fact the premise generates a
contradiction. Perhaps we are sound, but we cannot know unassailably
that we are sound."

So it seems Chalmers would have no problem with the "natural AI"
position he discussed earlier, that our reasoning could be
adequately captured by a computer simulation that did not come to
its top-level conclusions about mathematics via a strict axiom/proof
method involving the mathematical questions themselves, but rather
by some underlying fallible structure like a neural network. The
bottom-level behavior of the simulated neurons themselves would be
deducible given the initial state of the system using the axiom/
proof method, but that doesn't mean the system as a whole might not
make errors in mathematical calculations; see Douglas Hofstadter's
discussion of this issue starting on p. 571 of "Godel Escher Bach",
the section titled "Irrational and Rational Can Coexist on Different
Levels", where he writes:

"Another way to gain perspective on this is to remember that a
brain, too, is a collection of faultlessly functioning element-
neurons. Whenever a neuron's threshold is surpassed by the sum of
the incoming signals, BANG!-it fires. It never happens that a neuron
forgets its arithmetical knowledge-carelessly adding its inputs and
getting a wrong answer. Even when a neuron dies, it continues to
function correctly, in the sense that its components continue to
obey the laws of mathematics and physics. Yet as we all know,
neurons are perfectly capable of supporting high-level behavior that
is wrong, on its own level, in the most amazing ways. Figure 109 is
meant to illustrate such a class of levels: an incorrect belief held
in the software of a mind, supported by the hardware of a
faultlessly functioning brain."

Figure 109 depicts the outline of a person's head with "2+2=5"
appearing inside it, but the symbols in "2+2=5" are actually made up
of large collections of smaller mathematical equations, like
"7+7=14", which are all correct. A nice way of illustrating the
idea, I think.�

I came up with my own thought-experiment to show where Penrose's
argument goes wrong, based on the same conclusion that Chalmers
reached: a community of "realistic" AIs whose simulated brains work
similarly to real human brains would never be able to be 100%
certain that they had not reached a false conclusion about
arithmetic, and the very act of stating confidently in mathematical
that they would never reach a wrong conclusion would ensure that
they were endorsing a false proposition about arithmetic. See my
discussion with LauLuna on the "Penrose and algorithms" thread here: http://groups.google.com/group/everything-list/browse_thread/thread/c92723e0ef1a480c/429e70be57d2940b?#429e70be57d2940b

牋� Your paper is very interesting. It reminds me a lot of Stephen
Wolfram's cellular automaton theory. I only have one big problem
with it. The 10d manifold would be a single fixed structure that,
while conceivably capable of running the computations and/or
implementing the Peano arithmetic, has a problem with the role of
time in it. You might have a solution to this problem that I see
that I did not deduce as I read your paper. How do you define time
for your model?